knnMCN(TrnX, OrigTrnG, TstX = NULL, K = 1, ShowObs = F)The knnMCN function determines which class a undetermined case should belong to by following steps. First, calculate the Mahalanobis Distance between all the cases in training dataset. Then, select top K cases with nearest distances. Finally, these selected cases represent their classes and vote for the undetermined case under the principle of the minority is subordinate to the majority.
When calculating the Mahalanobis Distance, we use samples' covariance matrix (CM) and the Mahalanobis Distance is defined as follows:
MD=sqrt((X-Y)*inverse(CM)*transpose(X-Y)) , where X,Y are 1*n vectors and CM is n*n matrix.
Sometimes a case may get same "ballot" from class A and class B (even C, D, ...), this time a weighted voting process will be activated. The weight is based on the actual distance calculated between the test case and K cases in neighbor A and B. The test case belongs to the class with less total distance.
Also, to avoid unfair voting for undetermined case, K Threshold Value is stipulated to be less than the minimum size of the class in training dataset, or a warning will be shown.
knnVCN, dataFiller
library(knnGarden)
data(iris)
## Define data
TrnX=iris[c(1:20,80:100,140:150),1:4]
OrigTrnG=iris[c(1:20,80:100,140:150),5]
#
TstX<-iris[c(1:20,50:70,120:140),1:4]
#or
TstX<-NULL
## Call function
knnMCN(TrnX=TrnX,OrigTrnG=OrigTrnG,TstX=TstX,ShowObs=FALSE,K=5)
## The function is currently defined as
function (TrnX, OrigTrnG, TstX = NULL, K = 1, ShowObs = F)
{
OrigTrnG = as.factor(OrigTrnG)
TrnG = as.numeric(OrigTrnG)
CodeMeaning = data.frame(TrnG, OrigTrnG)
TK = sort(as.matrix(table(TrnG)), decreasing = F)
if (K > TK[1]) {
stop(c("\nNOTES: \nsorry, the value of K ", "(K=", K,
") ", "you have selected is bigger than the capacity of one class in your training data set",
"(", "the capacity is ", TK[1], ")", ",", "please choose a less value for K"))
}
if (is.null(TstX) == T) {
IsTst = 1
TstX <- as.matrix(TrnX)
}
else {
IsTst = 0
}
if (is.matrix(TstX) == F) {
TstX <- as.matrix(TstX)
}
TrnX <- as.matrix(TrnX)
ElmTrnG = union(TrnG, TrnG)
LevTrnG = length(ElmTrnG)
TrnTotal = cbind(TrnG, TrnX)
if (abs(det(cov(TrnX[which(TrnTotal[, 1] == ElmTrnG[1]),
]))) < 1e-07) {
stop("\nWarnings:\nsample variance-covariance matrix is singular,\nand larger class sample capacity is required ,\nor you can try other methods in knnWXM of this package")
}
else {
MaDisList = list(solve(cov(TrnX[which(TrnTotal[, 1] ==
ElmTrnG[1]), ]), LINPACK = T))
}
if (LevTrnG > 1) {
for (i in (1 + 1):LevTrnG) {
if (abs(det(cov(TrnX[which(TrnTotal[, 1] == ElmTrnG[i]),
]))) < 1e-07) {
stop("\nWarnings:\nsample variance-covariance matrix is singular,\nand larger class sample capacity is required ,\nor you can try other methods in knnWXM of this package")
}
else {
MaDisNode = list(solve(cov(TrnX[which(TrnTotal[,
1] == ElmTrnG[i]), ]), LINPACK = T))
MaDisList = c(MaDisList, MaDisNode)
}
}
}
NTstX = nrow(TstX)
NTrnTotal = nrow(TrnTotal)
VoteResult = NULL
VoteResultList = NULL
for (i in 1:nrow(TstX)) {
RankBoardI <- NULL
RankBoardIJ <- NULL
for (j in 1:LevTrnG) {
TempTrnXI = TrnX[which(TrnTotal[, 1] == ElmTrnG[j]),
]
TempCovJ = as.matrix(MaDisList[[j]])
TempTstXI = NULL
for (k in 1:nrow(TempTrnXI)) {
TempTstXI = rbind(TempTstXI, TstX[i, ])
}
TempMadisBoardI <- sqrt(diag((TempTstXI - TempTrnXI) %*%
TempCovJ %*% t(TempTstXI - TempTrnXI)))
MadisBoardI <- as.matrix(TempMadisBoardI)
GBoardI <- as.matrix(rep(ElmTrnG[j], nrow(TempTrnXI)))
RankBoardI <- cbind(GBoardI, MadisBoardI)
RankBoardIJ <- rbind(RankBoardIJ, RankBoardI)
}
VoteAndWeight = RankBoardIJ[sort(RankBoardIJ[, 2], index.return = T)$ix[1:k],
1:2]
TempVote4TstXI = RankBoardIJ[sort(RankBoardIJ[, 2], index.return = T)$ix[1:k],
1]
ElmVote = union(TempVote4TstXI, TempVote4TstXI)
CountVote = as.matrix(sort(table(TempVote4TstXI), decreasing = T))
TempWinner = as.numeric(rownames(CountVote))
if (length(CountVote) == 1 | K == 1) {
Winner = TempWinner[1]
TstXIBelong = union(CodeMeaning$OrigTrnG[which(CodeMeaning$TrnG ==
Winner)], CodeMeaning$OrigTrnG[which(CodeMeaning$TrnG ==
Winner)])
VoteResultNode = data.frame(TstXIBelong)
VoteResultList = rbind(VoteResultList, VoteResultNode)
}
else {
NumOfTie = CountVote[1]
FinalList = NULL
j = 1
TempWeight = sum(VoteAndWeight[which(VoteAndWeight[,
1] == TempWinner[j]), 2])
FinalList = data.frame(TempWinner[j], TempWeight)
while (CountVote[j] == CountVote[j + 1] & j < length(CountVote)) {
TempWeight = sum(VoteAndWeight[which(VoteAndWeight[,
1] == TempWinner[j + 1]), 2])
FinalListNode = c(TempWinner[j + 1], TempWeight)
FinalList = rbind(FinalList, FinalListNode)
j = j + 1
}
FinalList = FinalList[sort(FinalList$TempWeight,
index.return = T)$ix[1], ]
TstXIBelong = union(CodeMeaning$OrigTrnG[which(CodeMeaning$TrnG ==
FinalList[1, 1])], CodeMeaning$OrigTrnG[which(CodeMeaning$TrnG ==
FinalList[1, 1])])
VoteResultNode = data.frame(TstXIBelong)
VoteResultList = rbind(VoteResultList, VoteResultNode)
}
}
if (IsTst == 1) {
CheckT = as.matrix(table(data.frame(VoteResultList, OrigTrnG)))
AccuStat = 1 - sum(CheckT - diag(diag(CheckT)))/length(TrnG)
cat("test results", "\n")
print(CheckT)
cat("the classification accuracy of this algorithm on this training dataset is: ",
AccuStat * 100, "%", "\n\n\n")
}
if (IsTst == 1 & ShowObs == F) {
result = data.frame(VoteResultList, OrigTrnG)
}
else {
if (IsTst == 1 & ShowObs == T) {
result = data.frame(TstX, VoteResultList, OrigTrnG)
}
else {
if (ShowObs == F) {
result = data.frame(VoteResultList)
}
else {
result = data.frame(TstX, VoteResultList)
}
}
}
return(result)
}
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